Question

假设 $N$ 年的七月有五个星期一。下列哪一天一定会在 $N$ 年八月出现五次？（注意：两个月都有 $31$ 天。）

Suppose July of year $N$ has five Mondays. Which of the following must occur five times in August of year $N?$ (Note: both months have $31$ days.)

星期一

Monday

星期二

Tuesday

星期三

Wednesday

星期四

Thursday

星期五

Friday

答案：D

知识点：日期与时间模运算分类讨论

难度评级：1240

解答：

$31$ 天等于 $4$ 周又 $3$ 天，所以恰好是每月第 $1$ 、第 $2$ 、第 $3$ 日所对应的三个星期几会出现五次。

七月要有五个星期一，星期一就必须是七月第 $1$ 、第 $2$ 或第 $3$ 日。三种情况下，八月 $1$ 日分别是星期三、星期四或星期五，而八月出现五次的三个星期几都包括星期四。

也可以直接看出：七月有 $31$ 天，所以八月 $1$ 日与七月 $4$ 日是同一星期几。无论星期一是七月第 $1$ 、第 $2$ 还是第 $3$ 日，八月出现五次的三个星期几中总有星期四。

所以正确答案是 D。

A $31$ -day month is $4$ weeks plus $3$ extra days, so exactly the weekdays of the $1$ st, $2$ nd, and $3$ rd of the month occur five times.

For July to have five Mondays, Monday must be one of July $1,$ $2,$ or $3.$ In all three cases August $1$ lands on a Wednesday, Thursday, or Friday, and the common weekday among the resulting five-time days is Thursday.

More directly, since July has $31$ days, August $1$ is the same weekday as July $4.$ With Monday on July $1,$ $2,$ or $3,$ the three five-time weekdays of August always include Thursday.

Thus, the correct answer is D.

2002 AMC 10B 第 8 题

答案：D

难度评级：1240

解答：

其他年份的第 8 题